Question: Express this quotient in scientific notation: ${\frac{3.060\times 10^{-7}} {6.0\times 10^{-5}}}$
Explanation: Start by collecting like terms together. $= {\frac{3.060} {6.0}} \times{\frac{10^{-7}} {10^{-5}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.51 \times 10^{-7\,-\,-5}$ $= 0.51 \times 10^{-2}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.51$ is the same as $5.10 \div 10$ , or $5.10 \times 10^{-1}$ $ = {5.10 \times 10^{-1}} \times 10^{-2} $ $= 5.10\times 10^{-3}$